1. Open an existing file
2. Apply a morph change (like a “grow older” morph, or a “grow taller”, or a “grow fatter”)
3. Render the image to a file (png/jpeg)
4. Increase the morph again, save to a new file, etc,..

Ultimately I’d also like to to run DazStudio 4.5 so it invokes a script after start-up and exits when its done running. Most fully scriptable programs have a command line option to do this. Does DazScript?

All of those things can be done.
Regarding the script invocation at start-up, you can go to Edit->Preferences->Scene ad at the Load File drop-down you can browse to your custom script. I’ve never selected a script instead of a scene, myself, but script specific extensions are among the accepted extensions..